Optical Time-division multiplexing (0-TDM)

Chapter 2: MULTIPLEXING SCHEME AND NONLINEARITIES 15

2.2 Multichannel Communication systems

2.2.3 Optical Time-division multiplexing (0-TDM)

Time division multiplexing (TOM). is a type of digital or (rarely) analog multiplexing in which two or more signals or bit streams are transferred apparently simultaneously as sub- channels in one communication channel, but physically are taking turns on the channel. The time domain is divided into several recurrent time slots of fixed length, one for each sub- channel. A sample, byte or data block of sub-channel I is transmitted during time slot I, sub- channel 2 during timeslot 2, etc. One TOM frame consists of one time slot per sub-channel.

After the last sub-channel it starts allover again with a new frame, starting with the second sample, byte or data block from sub-channel I, etc.

An aIternative strategy for increasing the bit rate of digital optical fiber systems beyond the bandwidth capabilities of the drive electronics is known as optical time division mliltiplexing (aTDM).' A block schematic of an aTOM system which has demonstrated 16Gbps transmission over 8 krn is shown in Figure 2.3. The principle of this technique is to extend time division ~Iiltiplexing by optically combining a number of lower speed electronic base band digital channels. In the case illustrated in Figure, the optical multiplexing and de mliltiplexing ratio is 1.4, with a base band channel rate of 4Gbps.

4

GH.

clock

Timing

recovery

Error

lest

set

1

2

_{M DE}

2

U MU

X ^X

~

3

4 4

Fig 2.4: Four channel optical time division mliltiplexing (aTOM) fiber system.

2.2.4 Optical-CDMA (O-CDMA)

Instead of each channel occupying a given wavelength, frequency or time slot, each channel transmits its bits as a coded channel-specific sequence of plilses. This coded transmission typically is accomplished by transmitting a unique time-dependent series of short plilses.

These short plilsesare placed within chip times within the larger bit time. All channels, each

with a different code, can be transmitted on the same fiber and asynchronously

demliltip1exed. One effect of coding is that the frequency bandwidth of each channel is

broadbanded, or spread. If Iiltra-short «100 fs) optical plilses can be successfully generated

and modulated, then a significant fraction of the fiber bandwidth can be used. Unfortunately, it is difficult for the entire system to operate at these speeds without incurring enonrtoUScost and complexity.

Code division multiple access (CDMA), is a form of multiplexing (not a modulation scheme) and a method of multiple access that does not divide up the channel by time (as in TDMA), or frequency (as in FDMA), but instead encodes data with a special code associated with each channel and uses the constructive interference properties of the special codes to perform the multiplexing. CDMA also refers to digital cellular telephony systems that make use of this multiple access scheme such as those pioneered by Qualcomm, and W-CDMA by the International Telecommunication Union or lTV. CDMA has since been used in many communications systems, including the Global Positioning System (GPS) and in the OmniTRACS satellite system for transportation logistics.

Recently, CDMA has been also investigated to be employed in optical communication networks, especially in local access network (LAN). Current optical CDMA (O-CDMA), shown in figure 1.28,techniques fall into two categories, coherent and incoherent O-CDMA.

In incoherent O-CDMAunipolar codes (0, I) are used to modulate the power of optical signals. In coherent O-CDMA bipolar (-I, I) or multilevel codes are used to modulate the field of optical signals.

OCDMA is similar to PN-CDMA except that it employs a set of orthogonal sequences. such

as Walsh-Hadamard (WH) sequences, fot spectral spreading. The WH sequence length is

equal to the spreading factor N, which in tum is equal to the number of chips per transmitted

symbol. That is, unlike PN-CDMA, in which the spreading sequences look random,

spreading sequences in OCDMA are fully deterministic and repeat from one symbol to the

next. Provided the user signals are well synchronized in terms of symbol timing,

orthogonality of the spreading sequences guarantees that there is no mutual interference

between users. But the maximum number .oforthogonal sequences of length N being exactly

N, this is also the maximum number of users that can be accommodated (assuming again that

all users require a fixed bit rate equal to the chip rate divided by N). This implies that in terms

of the number of users which can be accommodated on a given channel. OCDMA is

equivalent to TDMA and FDMA. In optical CDMA system transmission, N users share the same channel medium.

2.2.5 Sub carrier multiplexing (SCM)

Optical sub carrier multiplexing (SCM) is a scheme where multiple signals are multiplexed in the RF domain and transmitted by a single wavelength. The most significant advantage of SCM in optical communications is its ability to place different optical carriers together closely. This is because microwave and RF devices are much more mature than optical devices: the stability ora microwave oscillator is much better than an optical oscillator (laser diode) and the frequency selectivity of a microwave filter is much better than an optical filter.

Therefore, the efficiency of bandwidth utilization of SCM is expected to be much better than conventional optical WDM.

SCM technology essentially uses a two step modulation. First, several low bandwidth RF channels carrying analog or digital signal are combined together and they are very close to each other in the frequency domain. Then this composite signal is further modulated onto a higher frequency microwave carrier or optical carrier and can be transmitted through different media. Because of its simple and low-cost implementation, high-speed optical data transmission using SCM technology attracted the attention of many researchers.

When the bandwidth of the information becomes higher, such as more than several GHz, and the transmission distance is very long, such as more than hundreds of kilometers, the DSB scheme will not work if it still use only a simple photon detector to detect. This is because the dispersion of the fiber will give quite different delay to +

if

and -

if

due to the large frequency difference between them. If the relative delay between

+ if

and -

if

is comparable to the duration of a baseband bit. then after photon detector, the two side bands will interfere with each other destructively. Two methods can be used to solve this problem, one way is to use narrow band optical filter to filter out each sub carrier channel and then detect them separately. This is the method used in previous study of high-speed data transmission utilizing SCM techniques. In those studies, DSB is used as the optical modulation method

and ASK is used as the RF modulation format. The demodulation of sub carrier is to filter out each sub carrier optically in order to avoid the fiber dispersion effect on the double side band modulation format. ASK RF modulation is used because it makes direct detection possible.

The optical spectrums of these systems are very similar to the spectrum showing in Figure a.

Another way is to use optical single side band modulation. The spectrum of optical single side band (OSSB) SCM the lower side band in the DSB spectrum is removed by ways such as optical filter or special modulating methods. The carrier itself could be removed or kept depending on the preferred demodulating method. The occupied spectrum is only half that of the optical DSB signal.

2.3 Fiber Nonlinearities

The response of any dielectric material to the light becomes nonlinear for intense electromagnetic fields. Fundamentally, the origin of nonlinear response is related to anharmonic motion of bound electrons under influence of an applied field. As a result, an intense light beam propagating through a fiber will induced a nonlinear polarization, which gives rise to nonlinear effect.

2.3.1 Self-Phase Modulation (SPM)

Self phase modulation (SPM) is due to the power dependence of the refractive index of the fiber core. SPM refers the self.induced phase shift experienced by an optical field during its propagation through the optical fiber; change of phase shift of an optical field is given by [I 8]

(2.1)

Where, ko '"

2;

^{and L} is the fiber length. ^~Lis the linear part and ^~Nl. is the nonlinear part that depends on intensity.

SPM interact with the chromatic dispersion in the fiber to change the rate at which the pulse broadens as it travels down the fiber. Whereas increasing the dispersion will reduce the impact of FWM, it will increase the impact of SPM. As an optical pulse travels down the

fiber, the leading edge of the pulse causes the refractive index of the fiber to rise causing a blue shift.

2.3.2 Cross Phase Modulation (XPM)

Cross phase modulation (XPM) is very similar to SPM except that it involves two pulses of light, whereas SPM needs only one pulse. In multi-channel WDM sy~ems, all the other interfering channels also modulate the refractive index of the channel under consideration, and therefore its phase. lIDs effect is called Cross Phase Modulation (XPM).

XPM refers the nonlinear phase shift .of an optical field induced by co-propagating channels at different wavelengths; the nonlinear phase shift be given as [18]

(2.2)

Where,

E,

and

E2

are the electric fields of two optical waves propagating through the same fiber with two different frequencies.

In XPM, two pulses travel down the fiber, each changing the refractive index as the optical power varies. If these two pulses happen to overlap, they will introduce distortion into the other pulses through XPM. Unlike, SPM, fiber dispersion has little impact on XPM.

Increasing the fiber effective area will improve XPM and all other fiber nonlinearities.

2.3.3 Four wave mixing (FWM):

Four-wave mixing (FWM) is a nonlinear process in optical fibers in which generally three

signal frequencies combine and produce several mixing products. It originates from the weak

dependence of the fiber refractive index on the intensity of the optical wave propagating

along the fiber through the third order non linear susceptibility .If three signal waves with

frequencies

fi ,

Jj,

fk

are incident at the fiber input , new waves are generated whose frequencies are

fijk=fi+jj -

fk .

(i,j, k = 1,2,3) (2.3)

Here we exclude fijk with i=k Ofj=k where interruptions from other channels to signal do not happen. As a result, we will examine FWM lights with the frequency of h2h!312,Jin,f132, h3I,

!i23,

!i21,f1l3, and.li 12which are shown in Fig. 2.5. Note that the number of the FWM

lights is enhanced drastically with an increase in the number of channels.

This is called "four wave mixing" since three waves .interfere to provide a fourth wave. Again it is sometimes called "four photon mixing".

fll3 fl12f123 fl f213

f221 f332 Optical frequency

Fig 2.5: Generated waves through fiber four wave mixing

Let four channels consist frequencies fa, /", fcand

fd.

The detailed explanation of FWM lights produced is as follows:

TABLE

2.1:

The FWM frequency combinations

Row No. l=a, j=b, k=c i=b,j=c, k=d i=c, j=d, k=a i=a,j=b, k=d

1

fabc~fa +/-fc ficd~fi +fc-fd /cdo=fc+/,rfa fabd=fa +fi-fd 2 /bca=fi +fc-fa /cdb=fc+f,rfi fdac=fd+/ ••fc fbtfa=fi +fd-fa

3

facb =fa+fc-fi, /bdc=fi +/,rfc / cad=fc+fa-fd fadb=fa+/,rfi

-

5

faae=fa+fa-fc fi,bd=fi,+fi,-fd feerfc+fc-fd faad=fa+j.-fd 6 fi,bc=fi, +fi,-fc fccb~fc+fc-fi, fdda~f~kfa fi,bd~fi, +fi,-fd 7 fi,ba=fi, +fi,-fa f ccd=fc+fc-fd fdda=fd+kfc fi,ba~fi, +fi,-fa

8

fcea=fc+fc-fa fddb=f~f,rfi, faae~fa+f.-fc fdda~f~f,rfa 9 fceb =fc+fc-fi, fddc=f~kfc faad=fa+f.-fd f<fdb=fd+f,rfi,

From the above table we can easily see that for each element in the last 6 rows there is an extra repetition. There are 24 elements in the last 6 rows. If we eliminate each extra repetition we will have 24-12=12 elements. From the upper 3 rows we get 3x4=12 individual combinations. So we get a total of 12+12=24 elements. So if we calculate using the previous equation 'C3x 9 = 36 we will get erroneous results. To eliminate this problem of calculating the total lights produced by FWM we developed an equation which gives the desired no of FWM lights without any error. The equation is as follows:

NumberofFWM lights = .C3 x9-n [(n_2)2 -1]

Where, n is the number of channels.

If we take the number of channels as n=4. If we put this value in equation no 1 we get the total no of FWM lights produced as 24 which verifies the validity of our equation. The equation has been also verified for various numbers of channels by a programme coded in C++.

900 792

S 800

-g,

700 605

:::i

600

:i 450

==

500-

•••

'0

..

400- 324

1:

300 224

E 200 147

:>

Z 100

9 24 0

3 4 5 6 7 8 9 10 11 12

Number of Channels

Fig 2.6: No. ofFWM Lights with increasing No. of Channels.

, ^, r~

_\

I I

!

Now ifthere are three channels of frequencies fa, fband fe, then the frequency components generated by FWM process are,

i,j,k=a,b,c and i,j#k (2.4)

The power of FWM signal for general case of WSK -WDM system can be found as [20]-

P

FWM 1024

n

^{2 [.} D X ¹¹¹¹ L ^{elf. ] 2} P P P ^-aL

=

-n-'-A,-2-C-2 - ---A---- ^{i j} k e '1.

elf

(2.5)

where, Aeffis the effective mode area, Pi, Pj and Pkare the input powers of channels i,j and k, n is the refractive index, A, is the wavelength, D is the degeneracy factor and Leff is the effective length of each fiber so that NLo=L is the length of each section, M is the number of span, N is the number of fiber in a span.

Necessity of channel coding:

Digital data transmission suffers from channel influence for the following aspect:

~ Severe (multipath) fading in terrestrial mobile radio communications

~ Very low signal-to-noise ratio for satellite communications due to high path loss and limited transmit power in the downlink

~ Compressed data (e.g. audio and video signals) is very sensitive to transmission errors.

~ To improve transmission performance, channel coding is added.

~ To optimize the use of the correction capacity of a particular code, soft decision is always a good solution.

~ Channel coding protects data against transmission errors to ensure adequate transmission quality (bit or frame error rate).

~ Channel coding is power efficient: Compared to the tmcoded case, the same errors rates are achieved with much less transmit power at the expense of a bandwidth expansion.

2.4 Convolution Coding:

In telecommunication, a convolutional code is a type of error.correcting code in which (a) each m-bit information symbol (each m-bit string) to be encoded is transformed into an n-bit symbol, where min is the code rate (n ~ m) and (b) the transformation is a function of the last k information symbols, where k is the constraint length of the code. Convolutional codes are often used to improve the performance of digital radio, mobile phones, satellite links, and Bluetooth implementation.

A free distance d is a minimal Hamming distance between different encoded sequences. A correcting capability t of a convolutional code is a number of errors that can be corrected by the code. Since a coDvolutionalcode doesn't use blocks, processing instead a continuous bitstream, the value of t applies to a quantity of errors located relatively near to each other.

That is, multiple groups of t errors can usually be fixed when they are relatively far. Free distance can be interpreted as a minimal length of an erroneous "burst" at the output of a convolutional decoder. Several algorithms exist for decoding convolutional codes. For relatively small values of k, the Viterbi algorithm is universally used as it provides maximum likelihood performance and is highly parallelizable. [21]

Wed) is obtained from the code weights in Table 2.2 as [12]' Substituting the unconditional BER (Pe) from Eq. (2.6) in Eq. (2.7b), we can calculate the coded BER from Eq. (2.6).

Table 2.2: Weigh Spectrum of convolutional encoders

Hamming Weight d Wid) for R~ll2 Wed) for R-1/3

10 3.6xl00¹

-

11 0

-

12 2.11xlOul

-

13 0

-

14 1.404x1Ou3

-

15 0 1.1

16 1.633xl0"" 1.6

17 0 1.9

18 7.7433 x 10⁰⁴ 2.8

19 0 5.5

20 5.0269xl0u^> 9.6

21 0 1.69xl0⁰²

22 3.322763 x lOuu 3.38xl0u,

23 0 6.36xl0u,

24 2.129291xl0u1 1.276xl0⁰³

25 0 2.172xlO^UJ

26 1.3436491 xl Ouo

-

Chapter 3

PERFORMANCE ANALYSIS

3.1 Introduction

The performance of a multichannel WSK-DWDM transmission system in presence of XPM & FWM has been evaluated in this chapter for binary and M-ary system. The system performance depends on various system parameters such as transmission power per channel, number of channel, fiber length; different channel spacing will be examined. Finally, the performance of WSK-DWDM system is compared for binary and M-ary coded and uncoded system with different parameters.

3.2: System Model:

The model of the WSK-DWDM system considered for analysis is shown in Fig 3.1.

o

M U X

,j, .<,

" M

i i U

1

i

X

: :

1)(

I

rataoolpul

Qia il'lXJl

Fig: 3.1: Block diagram basic WSK-DWDM transmission system.

The system is used to combine different signal carrier wavelengths onto a single fiber at one end and separate them onto their corresponding detectors at the other end.

Here MUX combine all of the signals and create a composite signal. This signal passes through the optical fiber and optical amplifier.

Optical amplifier amplifies an optical signal directly, without the need to first convert it to an electrical signal. An optical amplifier may be thought of as a laser without an optical cavity, or one in which feedback from the cavity is suppressed. Stimulated emission in the amplifier's gain medium causes amplification of incoming light.

DMUX separate them. Then at the .receiver we get all the signals individually.

3.3: Performance Analysis of a binary WSK-DWDM uncoded system

3.3.1: Receiver Model:

The Receiver Model of direct detection WSK-DWDM system is shown in fig 3.2.

-

^{OpticalSignal}

^c=Y

^III

=t> _{ill f}

Demodulated

MZI Ou1put

Amp6fiers& Baseband Comparator Equalizer Filter

Fig: 3.2: Block Diagram of a direct detection receiver with Mach-Zehnder Interferometer

(MZ1).

In the transmitter, the data of 10 Gbps is used to ditectly modulate a laser to generate the WSK signal which is transmitted through a single-mode fiber. At the receiving end, the received optical signal is detected by a Mach-Zehnder interferometer based direct detection receiver.

In the WSK direct detection receiver with MZI, the MZI act as an optical filter and differentially detect the 'mark' and 'space' of received WSK signal which are then directly ,.

fed to a pair of photo detectors. The difference of the two photo currents are applied to the amplifier which is followed by an equalizer. The equalizer is required to equalize the pulse shape distortion caused by the photo detector capacitance and due to the input resistance and capacitance of the amplifier. After passing through the baseband filter, the signal is detected at the decision circuit by comparing it with a threshold of zero value.

One other type of discriminator is the Fabry-Perot etalon interferometer; a small comparison in connection to direct detection would reveal some relevant aspects.

I. Mach-Zehnder Interferometer and Fabry-Perot etalon Interferometer both can act as tunable filter (for multichannel application) and optical discriminator.

II. The OFDs (MZI/FPI) are built with passive components which are less costly compared to heterodyne system.

III. MZI provides easy tunability in multichannel system compared to heterodyne system which requires LDs with wide tuning range and narrow LW.

IV. Receiver design is simple and less costly due to the absence of the sophisticated wideband IF circuits.

Operation of MZI:

It is a common property of the interference filter to transmit a narrow band of wave length and blocking of alI wavelengths outside the band. In our receiver, MZI is employed which is integrated with a silica wave guide. It is a very promising device in wavelength division multiplexing (WDM) and frequency division multiplexing (FDM) systems. Because of their high frequency selectivity without mechanical actuator (which is essential for an FPI). MZI's can be series cascaded to achieve increase transmission capacity [22]'

MZI has two input ports, two output ports, 3 dB couplers and two waveguide arms with length difference AL. A thin film heater is placed in one of the arms to act as a phase shifter, because light path length of heated wave guide arm changes due to the change of refractive index. The phase shifter is used for precise frequency tnning. Frequency spacing of the peak